{"paper":{"title":"Heat kernel of supercritical SDEs with unbounded drifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"HSE), St\\'ephane Menozzi (LaMME, Zhang Xicheng","submitted_at":"2020-12-29T14:40:23Z","abstract_excerpt":"Let $\\alpha\\in(0,2)$ and $d\\in{\\mathbb N}$. Consider the following SDE in ${\\mathbb R}^d$:$${\\rm d}X_t=b(t,X_t){\\rm d} t+a(t,X_{t-}){\\rm d} L^{(\\alpha)}_t,\\ \\ X_0=x,$$where $L^{(\\alpha)}$ is a $d$-dimensional rotationally invariant  $\\alpha$-stable process, $b:{\\mathbb R}_+\\times{\\mathbb R}^d\\to{\\mathbb R}^d$ and $a:{\\mathbb R}_+\\times{\\mathbb R}^d\\to{\\mathbb R}^d\\otimes{\\mathbb R}^d$ are  H{\\\"o}lder continuous functions in space, with respective order $\\beta,\\gamma\\in (0,1)$ such that $(\\beta\\wedge \\gamma)+\\alpha>1$,  uniformly in $t$.  Here $b$ may be unbounded.When $a$ is bounded and unifor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.14775","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2012.14775/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}